LMFDB - Embedded newform 369.2.u.a.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [369,2,Mod(46,369)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(369, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 11]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("369.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 369 = 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	369.u (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.94647983459$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			361.3
Character	$\chi$	$=$	369.361
Dual form			369.2.u.a.46.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00762 - 1.38687i) q^{2} +(-0.290083 - 0.892782i) q^{4} +(2.57687 - 0.837277i) q^{5} +(-0.252316 + 1.59306i) q^{7} +(1.73027 + 0.562198i) q^{8} +O(q^{10})$	\(q+(1.00762 - 1.38687i) q^{2} +(-0.290083 - 0.892782i) q^{4} +(2.57687 - 0.837277i) q^{5} +(-0.252316 + 1.59306i) q^{7} +(1.73027 + 0.562198i) q^{8} +(1.43532 - 4.41746i) q^{10} +(-0.314590 - 0.617417i) q^{11} +(-1.50733 + 0.238738i) q^{13} +(1.95513 + 1.95513i) q^{14} +(4.04205 - 2.93672i) q^{16} +(-0.942631 + 0.480295i) q^{17} +(-0.126968 - 0.0201098i) q^{19} +(-1.49501 - 2.05771i) q^{20} +(-1.17327 - 0.185828i) q^{22} +(-1.52374 - 1.10707i) q^{23} +(1.89416 - 1.37619i) q^{25} +(-1.18772 + 2.33104i) q^{26} +(1.49545 - 0.236856i) q^{28} +(-7.39222 - 3.76652i) q^{29} +(0.373094 - 1.14827i) q^{31} -4.92630i q^{32} +(-0.283709 + 1.79127i) q^{34} +(0.683646 + 4.31637i) q^{35} +(-1.86889 - 5.75186i) q^{37} +(-0.155826 + 0.155826i) q^{38} +4.92939 q^{40} +(-5.96866 - 2.31844i) q^{41} +(-6.21829 + 8.55874i) q^{43} +(-0.459962 + 0.459962i) q^{44} +(-3.07072 + 0.997738i) q^{46} +(0.991818 + 6.26210i) q^{47} +(4.18322 + 1.35921i) q^{49} -4.01364i q^{50} +(0.650391 + 1.27646i) q^{52} +(11.1289 + 5.67046i) q^{53} +(-1.32761 - 1.32761i) q^{55} +(-1.33219 + 2.61457i) q^{56} +(-12.6723 + 6.45684i) q^{58} +(6.61738 + 4.80781i) q^{59} +(-1.54768 - 2.13021i) q^{61} +(-1.21656 - 1.67445i) q^{62} +(1.25193 + 0.909582i) q^{64} +(-3.68431 + 1.87725i) q^{65} +(-3.85439 + 7.56467i) q^{67} +(0.702239 + 0.702239i) q^{68} +(6.67512 + 3.40115i) q^{70} +(-1.94789 - 3.82296i) q^{71} -12.1957i q^{73} +(-9.86025 - 3.20379i) q^{74} +(0.0188776 + 0.119188i) q^{76} +(1.06296 - 0.345376i) q^{77} +(-8.14191 + 8.14191i) q^{79} +(7.95700 - 10.9519i) q^{80} +(-9.22954 + 5.94167i) q^{82} -6.49090 q^{83} +(-2.02690 + 2.02690i) q^{85} +(5.60421 + 17.2480i) q^{86} +(-0.197214 - 1.24516i) q^{88} +(-0.451128 + 2.84831i) q^{89} -2.46150i q^{91} +(-0.546357 + 1.68151i) q^{92} +(9.68412 + 4.93431i) q^{94} +(-0.344018 + 0.0544871i) q^{95} +(0.548878 - 1.07723i) q^{97} +(6.10017 - 4.43203i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/369\mathbb{Z}\right)^\times$.

$n$	$83$	$334$
$\chi(n)$	$1$	$e\left(\frac{9}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00762	−	1.38687i	0.712497	−	0.980669i	−0.287242	−	0.957858i	$-0.592739\pi$
$2$	1.00762	−	1.38687i	0.712497	−	0.980669i	0.999740	−	0.0228107i	$-0.00726149\pi$
$3$		0			0
$3$		0			0
$4$	−0.290083	−	0.892782i	−0.145041	−	0.446391i
$5$	2.57687	−	0.837277i	1.15241	−	0.374442i	0.330361	−	0.943855i	$-0.392829\pi$
$5$	2.57687	−	0.837277i	1.15241	−	0.374442i	0.822052	+	0.569413i	$0.192829\pi$
$6$		0			0
$7$	−0.252316	+	1.59306i	−0.0953664	+	0.602120i	0.893003	+	0.450050i	$0.148594\pi$
$7$	−0.252316	+	1.59306i	−0.0953664	+	0.602120i	−0.988370	+	0.152070i	$0.951406\pi$
$8$	1.73027	+	0.562198i	0.611742	+	0.198767i
$9$		0			0
$10$	1.43532	−	4.41746i	0.453888	−	1.39692i
$11$	−0.314590	−	0.617417i	−0.0948524	−	0.186158i	0.838705	−	0.544586i	$-0.183313\pi$
$11$	−0.314590	−	0.617417i	−0.0948524	−	0.186158i	−0.933558	+	0.358427i	$0.883313\pi$
$12$		0			0
$13$	−1.50733	+	0.238738i	−0.418058	+	0.0662139i	−0.361920	−	0.932209i	$-0.617879\pi$
$13$	−1.50733	+	0.238738i	−0.418058	+	0.0662139i	−0.0561381	+	0.998423i	$0.517879\pi$
$14$	1.95513	+	1.95513i	0.522532	+	0.522532i
$15$		0			0
$16$	4.04205	−	2.93672i	1.01051	−	0.734180i
$17$	−0.942631	+	0.480295i	−0.228622	+	0.116489i	−0.564550	−	0.825399i	$-0.690950\pi$
$17$	−0.942631	+	0.480295i	−0.228622	+	0.116489i	0.335928	+	0.941888i	$0.390950\pi$
$18$		0			0
$19$	−0.126968	−	0.0201098i	−0.0291285	−	0.00461350i	0.141853	−	0.989888i	$-0.454694\pi$
$19$	−0.126968	−	0.0201098i	−0.0291285	−	0.00461350i	−0.170982	+	0.985274i	$0.554694\pi$
$20$	−1.49501	−	2.05771i	−0.334295	−	0.460117i
$21$		0			0
$22$	−1.17327	−	0.185828i	−0.250142	−	0.0396186i
$23$	−1.52374	−	1.10707i	−0.317723	−	0.230839i	0.417480	−	0.908686i	$-0.362913\pi$
$23$	−1.52374	−	1.10707i	−0.317723	−	0.230839i	−0.735203	+	0.677847i	$0.762913\pi$
$24$		0			0
$25$	1.89416	−	1.37619i	0.378831	−	0.275237i
$26$	−1.18772	+	2.33104i	−0.232932	+	0.457154i
$27$		0			0
$28$	1.49545	−	0.236856i	0.282613	−	0.0447615i
$29$	−7.39222	−	3.76652i	−1.37270	−	0.699426i	−0.396853	−	0.917882i	$-0.629898\pi$
$29$	−7.39222	−	3.76652i	−1.37270	−	0.699426i	−0.975847	+	0.218456i	$0.929898\pi$
$30$		0			0
$31$	0.373094	−	1.14827i	0.0670097	−	0.206235i	−0.911945	−	0.410313i	$-0.865420\pi$
$31$	0.373094	−	1.14827i	0.0670097	−	0.206235i	0.978955	+	0.204078i	$0.0654196\pi$
$32$		−	4.92630i		−	0.870855i
$33$		0			0
$34$	−0.283709	+	1.79127i	−0.0486557	+	0.307200i
$35$	0.683646	+	4.31637i	0.115557	+	0.729600i
$36$		0			0
$37$	−1.86889	−	5.75186i	−0.307244	−	0.945600i	−0.978830	−	0.204673i	$-0.934387\pi$
$37$	−1.86889	−	5.75186i	−0.307244	−	0.945600i	0.671586	−	0.740926i	$-0.265613\pi$
$38$	−0.155826	+	0.155826i	−0.0252783	+	0.0252783i
$39$		0			0
$40$	4.92939			0.779405
$41$	−5.96866	−	2.31844i	−0.932147	−	0.362079i
$41$	−5.96866	−	2.31844i	−0.932147	−	0.362079i
$42$		0			0
$43$	−6.21829	+	8.55874i	−0.948280	+	1.30520i	0.00400713	+	0.999992i	$0.498724\pi$
$43$	−6.21829	+	8.55874i	−0.948280	+	1.30520i	−0.952287	+	0.305204i	$0.901276\pi$
$44$	−0.459962	+	0.459962i	−0.0693419	+	0.0693419i
$45$		0			0
$46$	−3.07072	+	0.997738i	−0.452753	+	0.147108i
$47$	0.991818	+	6.26210i	0.144672	+	0.913421i	0.948089	+	0.318005i	$0.103013\pi$
$47$	0.991818	+	6.26210i	0.144672	+	0.913421i	−0.803418	+	0.595416i	$0.796987\pi$
$48$		0			0
$49$	4.18322	+	1.35921i	0.597603	+	0.194173i
$50$		−	4.01364i		−	0.567614i
$51$		0			0
$52$	0.650391	+	1.27646i	0.0901930	+	0.177014i
$53$	11.1289	+	5.67046i	1.52867	+	0.778898i	0.997654	−	0.0684612i	$-0.0218089\pi$
$53$	11.1289	+	5.67046i	1.52867	+	0.778898i	0.531020	+	0.847359i	$0.321809\pi$
$54$		0			0
$55$	−1.32761	−	1.32761i	−0.179015	−	0.179015i
$56$	−1.33219	+	2.61457i	−0.178021	+	0.349386i
$57$		0			0
$58$	−12.6723	+	6.45684i	−1.66395	+	0.847825i
$59$	6.61738	+	4.80781i	0.861509	+	0.625923i	0.928295	−	0.371844i	$-0.121274\pi$
$59$	6.61738	+	4.80781i	0.861509	+	0.625923i	−0.0667860	+	0.997767i	$0.521274\pi$
$60$		0			0
$61$	−1.54768	−	2.13021i	−0.198161	−	0.272745i	0.698360	−	0.715747i	$-0.253913\pi$
$61$	−1.54768	−	2.13021i	−0.198161	−	0.272745i	−0.896521	+	0.443002i	$0.853913\pi$
$62$	−1.21656	−	1.67445i	−0.154504	−	0.212656i
$63$		0			0
$64$	1.25193	+	0.909582i	0.156491	+	0.113698i
$65$	−3.68431	+	1.87725i	−0.456982	+	0.232844i
$66$		0			0
$67$	−3.85439	+	7.56467i	−0.470889	+	0.924172i	0.526375	+	0.850252i	$0.323551\pi$
$67$	−3.85439	+	7.56467i	−0.470889	+	0.924172i	−0.997264	+	0.0739193i	$0.976449\pi$
$68$	0.702239	+	0.702239i	0.0851590	+	0.0851590i
$69$		0			0
$70$	6.67512	+	3.40115i	0.797830	+	0.406515i
$71$	−1.94789	−	3.82296i	−0.231172	−	0.453701i	0.746058	−	0.665881i	$-0.231944\pi$
$71$	−1.94789	−	3.82296i	−0.231172	−	0.453701i	−0.977231	+	0.212179i	$0.931944\pi$
$72$		0			0
$73$		−	12.1957i		−	1.42739i	−0.700455	−	0.713697i	$-0.747019\pi$
$73$		−	12.1957i		−	1.42739i	0.700455	−	0.713697i	$-0.252981\pi$
$74$	−9.86025	−	3.20379i	−1.14623	−	0.372433i
$75$		0			0
$76$	0.0188776	+	0.119188i	0.00216541	+	0.0136718i
$77$	1.06296	−	0.345376i	0.121135	−	0.0393593i
$78$		0			0
$79$	−8.14191	+	8.14191i	−0.916037	+	0.916037i	−0.996738	−	0.0807015i	$-0.974284\pi$
$79$	−8.14191	+	8.14191i	−0.916037	+	0.916037i	0.0807015	+	0.996738i	$0.474284\pi$
$80$	7.95700	−	10.9519i	0.889619	−	1.22446i
$81$		0			0
$82$	−9.22954	+	5.94167i	−1.01923	+	0.656147i
$83$	−6.49090			−0.712469			−0.356235	−	0.934397i	$-0.615940\pi$
$83$	−6.49090			−0.712469			−0.356235	+	0.934397i	$0.615940\pi$
$84$		0			0
$85$	−2.02690	+	2.02690i	−0.219848	+	0.219848i
$86$	5.60421	+	17.2480i	0.604317	+	1.85990i
$87$		0			0
$88$	−0.197214	−	1.24516i	−0.0210231	−	0.132734i
$89$	−0.451128	+	2.84831i	−0.0478195	+	0.301920i	−0.999993	−	0.00363635i	$-0.998843\pi$
$89$	−0.451128	+	2.84831i	−0.0478195	+	0.301920i	0.952174	+	0.305557i	$0.0988425\pi$
$90$		0			0
$91$		−	2.46150i		−	0.258036i
$92$	−0.546357	+	1.68151i	−0.0569616	+	0.175310i
$93$		0			0
$94$	9.68412	+	4.93431i	0.998841	+	0.508935i
$95$	−0.344018	+	0.0544871i	−0.0352955	+	0.00559026i
$96$		0			0
$97$	0.548878	−	1.07723i	0.0557301	−	0.109377i	−0.861462	−	0.507823i	$-0.830450\pi$
$97$	0.548878	−	1.07723i	0.0557301	−	0.109377i	0.917192	+	0.398446i	$0.130450\pi$
$98$	6.10017	−	4.43203i	0.616210	−	0.447703i
$99$		0			0
$100$	−1.77810	−	1.29186i	−0.177810	−	0.129186i
$101$	5.23645	+	0.829373i	0.521047	+	0.0825257i	0.411418	−	0.911447i	$-0.365034\pi$
$101$	5.23645	+	0.829373i	0.521047	+	0.0825257i	0.109629	+	0.993973i	$0.465034\pi$
$102$		0			0
$103$	8.15642	+	11.2264i	0.803676	+	1.10617i	0.992268	+	0.124110i	$0.0396075\pi$
$103$	8.15642	+	11.2264i	0.803676	+	1.10617i	−0.188592	+	0.982055i	$0.560392\pi$
$104$	−2.74230	−	0.434338i	−0.268905	−	0.0425903i
$105$		0			0
$106$	19.0780	−	9.72072i	1.85302	−	0.944159i
$107$	7.71269	−	5.60360i	0.745614	−	0.541720i	−0.148850	−	0.988860i	$-0.547557\pi$
$107$	7.71269	−	5.60360i	0.745614	−	0.541720i	0.894464	+	0.447139i	$0.147557\pi$
$108$		0			0
$109$	−1.66630	−	1.66630i	−0.159603	−	0.159603i	0.622788	−	0.782391i	$-0.286000\pi$
$109$	−1.66630	−	1.66630i	−0.159603	−	0.159603i	−0.782391	+	0.622788i	$0.786000\pi$
$110$	−3.17895	+	0.503497i	−0.303101	+	0.0480065i
$111$		0			0
$112$	3.65850	+	7.18020i	0.345695	+	0.678465i
$113$	2.37239	−	7.30147i	0.223176	−	0.686865i	−0.775296	−	0.631598i	$-0.782399\pi$
$113$	2.37239	−	7.30147i	0.223176	−	0.686865i	0.998472	−	0.0552663i	$-0.0176008\pi$
$114$		0			0
$115$	−4.85342	−	1.57697i	−0.452583	−	0.147053i
$116$	−1.21833	+	7.69224i	−0.113119	+	0.714207i
$117$		0			0
$118$	13.3356	−	4.33302i	1.22765	−	0.398886i
$119$	−0.527297	−	1.62285i	−0.0483372	−	0.148767i
$120$		0			0
$121$	6.18340	−	8.51072i	0.562127	−	0.773702i
$122$	−4.51381			−0.408661
$123$		0			0
$124$	−1.13338			−0.101781
$125$	−4.23422	+	5.82791i	−0.378720	+	0.521264i
$126$		0			0
$127$	−1.92578	−	5.92695i	−0.170886	−	0.525932i	0.828536	−	0.559936i	$-0.189174\pi$
$127$	−1.92578	−	5.92695i	−0.170886	−	0.525932i	−0.999422	+	0.0340038i	$0.989174\pi$
$128$	11.8933	−	3.86438i	1.05123	−	0.341566i
$129$		0			0
$130$	−1.10889	+	7.00124i	−0.0972558	+	0.614049i
$131$	−0.689839	−	0.224142i	−0.0602715	−	0.0195834i	0.278726	−	0.960371i	$-0.410088\pi$
$131$	−0.689839	−	0.224142i	−0.0602715	−	0.0195834i	−0.338998	+	0.940787i	$0.610088\pi$
$132$		0			0
$133$	0.0640721	−	0.197194i	0.00555576	−	0.0170989i
$134$	6.60748	+	12.9679i	0.570799	+	1.12026i
$135$		0			0
$136$	−1.90102	+	0.301093i	−0.163011	+	0.0258185i
$137$	−13.1949	−	13.1949i	−1.12731	−	1.12731i	−0.990612	−	0.136700i	$-0.956350\pi$
$137$	−13.1949	−	13.1949i	−1.12731	−	1.12731i	−0.136700	−	0.990612i	$-0.543650\pi$
$138$		0			0
$139$	−5.13170	+	3.72840i	−0.435265	+	0.316239i	−0.783751	−	0.621075i	$-0.786696\pi$
$139$	−5.13170	+	3.72840i	−0.435265	+	0.316239i	0.348486	+	0.937314i	$0.386696\pi$
$140$	3.65527	−	1.86245i	0.308926	−	0.157406i
$141$		0			0
$142$	−7.26470	−	1.15062i	−0.609640	−	0.0965576i
$143$	0.621592	+	0.855548i	0.0519801	+	0.0715445i
$144$		0			0
$145$	−22.2024	−	3.51652i	−1.84381	−	0.292031i
$146$	−16.9139	−	12.2886i	−1.39980	−	1.01701i
$147$		0			0
$148$	−4.59302	+	3.33703i	−0.377544	+	0.274302i
$149$	−5.86949	+	11.5195i	−0.480848	+	0.943717i	0.515382	+	0.856961i	$0.327650\pi$
$149$	−5.86949	+	11.5195i	−0.480848	+	0.943717i	−0.996230	+	0.0867562i	$0.972350\pi$
$150$		0			0
$151$	−1.37899	+	0.218411i	−0.112221	+	0.0177740i	−0.212292	−	0.977206i	$-0.568093\pi$
$151$	−1.37899	+	0.218411i	−0.112221	+	0.0177740i	0.100071	+	0.994980i	$0.468093\pi$
$152$	−0.208383	−	0.106176i	−0.0169021	−	0.00861205i
$153$		0			0
$154$	0.592069	−	1.82220i	0.0477102	−	0.146837i
$155$		−	3.27132i		−	0.262759i
$156$		0			0
$157$	2.74716	−	17.3449i	0.219247	−	1.38427i	−0.594987	−	0.803735i	$-0.702843\pi$
$157$	2.74716	−	17.3449i	0.219247	−	1.38427i	0.814234	−	0.580537i	$-0.197157\pi$
$158$	3.08783	+	19.4958i	0.245655	+	1.55100i
$159$		0			0
$160$	−4.12468	−	12.6945i	−0.326084	−	1.00358i
$161$	2.14809	−	2.14809i	0.169293	−	0.169293i
$162$		0			0
$163$	17.6081			1.37918			0.689588	−	0.724202i	$-0.257792\pi$
$163$	17.6081			1.37918			0.689588	+	0.724202i	$0.257792\pi$
$164$	−0.338458	+	6.00125i	−0.0264291	+	0.468619i
$165$		0			0
$166$	−6.54039	+	9.00207i	−0.507632	+	0.698696i
$167$	1.96297	−	1.96297i	0.151899	−	0.151899i	−0.627066	−	0.778966i	$-0.715745\pi$
$167$	1.96297	−	1.96297i	0.151899	−	0.151899i	0.778966	+	0.627066i	$0.215745\pi$
$168$		0			0
$169$	−10.1487	+	3.29751i	−0.780668	+	0.253654i
$170$	0.768705	+	4.85341i	0.0589570	+	0.372240i
$171$		0			0
$172$	9.44491	+	3.06884i	0.720168	+	0.233997i
$173$		−	11.7096i		−	0.890265i	−0.895465	−	0.445132i	$-0.853157\pi$
$173$		−	11.7096i		−	0.890265i	0.895465	−	0.445132i	$-0.146843\pi$
$174$		0			0
$175$	1.71442	+	3.36474i	0.129598	+	0.254350i
$176$	−3.08477	−	1.57177i	−0.232523	−	0.118476i
$177$		0			0
$178$	3.49568	+	3.49568i	0.262012	+	0.262012i
$179$	−1.93111	+	3.79002i	−0.144338	+	0.283279i	−0.951846	−	0.306578i	$-0.900816\pi$
$179$	−1.93111	+	3.79002i	−0.144338	+	0.283279i	0.807508	+	0.589857i	$0.200816\pi$
$180$		0			0
$181$	4.13089	−	2.10479i	0.307047	−	0.156448i	−0.293677	−	0.955905i	$-0.594879\pi$
$181$	4.13089	−	2.10479i	0.307047	−	0.156448i	0.600724	+	0.799457i	$0.294879\pi$
$182$	−3.41380	−	2.48027i	−0.253048	−	0.183850i
$183$		0			0
$184$	−2.01409	−	2.77216i	−0.148481	−	0.204367i
$185$	−9.63179	−	13.2570i	−0.708144	−	0.974676i
$186$		0			0
$187$	0.593084	+	0.430901i	0.0433706	+	0.0315106i
$188$	5.30298	−	2.70200i	0.386760	−	0.197064i
$189$		0			0
$190$	−0.271074	+	0.532013i	−0.0196658	+	0.0385963i
$191$	−15.8171	−	15.8171i	−1.14449	−	1.14449i	−0.987619	−	0.156869i	$-0.949860\pi$
$191$	−15.8171	−	15.8171i	−1.14449	−	1.14449i	−0.156869	−	0.987619i	$-0.550140\pi$
$192$		0			0
$193$	12.9855	+	6.61647i	0.934720	+	0.476264i	0.853884	−	0.520464i	$-0.174241\pi$
$193$	12.9855	+	6.61647i	0.934720	+	0.476264i	0.0808362	+	0.996727i	$0.474241\pi$
$194$	−0.940926	−	1.84667i	−0.0675546	−	0.132583i
$195$		0			0
$196$		−	4.12899i		−	0.294928i
$197$	−0.885009	−	0.287557i	−0.0630543	−	0.0204876i	0.277320	−	0.960778i	$-0.410554\pi$
$197$	−0.885009	−	0.287557i	−0.0630543	−	0.0204876i	−0.340374	+	0.940290i	$0.610554\pi$
$198$		0			0
$199$	0.0644895	+	0.407171i	0.00457154	+	0.0288636i	0.989869	−	0.141986i	$-0.0453488\pi$
$199$	0.0644895	+	0.407171i	0.00457154	+	0.0288636i	−0.985297	+	0.170850i	$0.945349\pi$
$200$	4.05109	−	1.31628i	0.286455	−	0.0930749i
$201$		0			0
$202$	6.42661	−	6.42661i	0.452175	−	0.452175i
$203$	7.86547	−	10.8259i	0.552048	−	0.759828i
$204$		0			0
$205$	−17.3216	−	0.976904i	−1.20980	−	0.0682299i
$206$	23.7881			1.65740
$207$		0			0
$208$	−5.39160	+	5.39160i	−0.373840	+	0.373840i
$209$	0.0275268	+	0.0847187i	0.00190407	+	0.00586011i
$210$		0			0
$211$	−3.50778	−	22.1473i	−0.241486	−	1.52468i	−0.748728	−	0.662877i	$-0.769335\pi$
$211$	−3.50778	−	22.1473i	−0.241486	−	1.52468i	0.507243	−	0.861803i	$-0.330665\pi$
$212$	1.83419	−	11.5806i	0.125972	−	0.795359i
$213$		0			0
$214$		−	16.3429i		−	1.11717i
$215$	−8.85770	+	27.2612i	−0.604090	+	1.85920i
$216$		0			0
$217$	1.73512	+	0.884087i	0.117788	+	0.0600157i
$218$	−3.98995	+	0.631946i	−0.270234	+	0.0428008i
$219$		0			0
$220$	−0.800149	+	1.57038i	−0.0539460	+	0.105875i
$221$	1.30619	−	0.949004i	0.0878640	−	0.0638369i
$222$		0			0
$223$	3.29767	+	2.39590i	0.220829	+	0.160441i	0.692700	−	0.721226i	$-0.256421\pi$
$223$	3.29767	+	2.39590i	0.220829	+	0.160441i	−0.471871	+	0.881668i	$0.656421\pi$
$224$	7.84789	+	1.24298i	0.524359	+	0.0830504i
$225$		0			0
$226$	−7.73575	−	10.6473i	−0.514574	−	0.708251i
$227$	21.3270	+	3.37787i	1.41552	+	0.224197i	0.816875	−	0.576815i	$-0.195705\pi$
$227$	21.3270	+	3.37787i	1.41552	+	0.224197i	0.598649	+	0.801012i	$0.295705\pi$
$228$		0			0
$229$	8.82761	−	4.49789i	0.583345	−	0.297229i	−0.137304	−	0.990529i	$-0.543844\pi$
$229$	8.82761	−	4.49789i	0.583345	−	0.297229i	0.720649	+	0.693300i	$0.243844\pi$
$230$	−7.07748	+	5.14209i	−0.466675	+	0.339059i
$231$		0			0
$232$	−10.6730	−	10.6730i	−0.700715	−	0.700715i
$233$	1.27079	−	0.201273i	0.0832521	−	0.0131858i	−0.114669	−	0.993404i	$-0.536581\pi$
$233$	1.27079	−	0.201273i	0.0832521	−	0.0131858i	0.197922	+	0.980218i	$0.436581\pi$
$234$		0			0
$235$	7.79890	+	15.3062i	0.508744	+	0.998466i
$236$	2.37274	−	7.30254i	0.154452	−	0.475355i
$237$		0			0
$238$	−2.78201	−	0.903930i	−0.180331	−	0.0585931i
$239$	1.11016	−	7.00929i	0.0718104	−	0.453393i	−0.925415	−	0.378955i	$-0.876284\pi$
$239$	1.11016	−	7.00929i	0.0718104	−	0.453393i	0.997226	−	0.0744383i	$-0.0237164\pi$
$240$		0			0
$241$	10.2597	−	3.33359i	0.660888	−	0.214735i	0.0406791	−	0.999172i	$-0.487048\pi$
$241$	10.2597	−	3.33359i	0.660888	−	0.214735i	0.620209	+	0.784437i	$0.287048\pi$
$242$	−5.57276	−	17.1512i	−0.358231	−	1.10252i
$243$		0			0
$244$	−1.45285	+	1.99968i	−0.0930094	+	0.128016i
$245$	11.9177			0.761391
$246$		0			0
$247$	0.196184			0.0124829
$248$	1.29111	−	1.77705i	0.0819853	−	0.112843i
$249$		0			0
$250$	3.81608	+	11.7447i	0.241350	+	0.742798i
$251$	−5.35009	+	1.73835i	−0.337695	+	0.109724i	−0.472955	−	0.881086i	$-0.656813\pi$
$251$	−5.35009	+	1.73835i	−0.337695	+	0.109724i	0.135261	+	0.990810i	$0.456813\pi$
$252$		0			0
$253$	−0.204167	+	1.28906i	−0.0128359	+	0.0810424i
$254$	−10.1604	−	3.30132i	−0.637520	−	0.207143i
$255$		0			0
$256$	5.66820	−	17.4449i	0.354263	−	1.09031i
$257$	9.98071	+	19.5882i	0.622580	+	1.22188i	0.959861	+	0.280477i	$0.0904927\pi$
$257$	9.98071	+	19.5882i	0.622580	+	1.22188i	−0.337281	+	0.941404i	$0.609507\pi$
$258$		0			0
$259$	9.63460	−	1.52597i	0.598665	−	0.0948192i
$260$	2.74473	+	2.74473i	0.170221	+	0.170221i
$261$		0			0
$262$	−1.00596	+	0.730869i	−0.0621481	+	0.0451533i
$263$	−5.22227	+	2.66088i	−0.322019	+	0.164077i	−0.607526	−	0.794300i	$-0.707838\pi$
$263$	−5.22227	+	2.66088i	−0.322019	+	0.164077i	0.285507	+	0.958377i	$0.407838\pi$
$264$		0			0
$265$	33.4255	+	5.29409i	2.05331	+	0.325213i
$266$	−0.208922	−	0.287557i	−0.0128099	−	0.0176313i
$267$		0			0
$268$	7.87170	+	1.24675i	0.480840	+	0.0761576i
$269$	11.1080	+	8.07042i	0.677265	+	0.492062i	0.872449	−	0.488705i	$-0.162530\pi$
$269$	11.1080	+	8.07042i	0.677265	+	0.492062i	−0.195184	+	0.980767i	$0.562530\pi$
$270$		0			0
$271$	12.8738	−	9.35335i	0.782026	−	0.568175i	−0.123560	−	0.992337i	$-0.539431\pi$
$271$	12.8738	−	9.35335i	0.782026	−	0.568175i	0.905586	+	0.424162i	$0.139431\pi$
$272$	−2.39967	+	4.70962i	−0.145501	+	0.285562i
$273$		0			0
$274$	−31.5951	+	5.00417i	−1.90873	+	0.302313i
$275$	−1.44556	−	0.736551i	−0.0871708	−	0.0444157i
$276$		0			0
$277$	−5.93200	+	18.2568i	−0.356420	+	1.09695i	0.598762	+	0.800927i	$0.295659\pi$
$277$	−5.93200	+	18.2568i	−0.356420	+	1.09695i	−0.955182	+	0.296020i	$0.904341\pi$
$278$			10.8738i			0.652170i
$279$		0			0
$280$	−1.24376	+	7.85282i	−0.0743291	+	0.469296i
$281$	0.226991	+	1.43316i	0.0135411	+	0.0854954i	0.993533	−	0.113540i	$-0.0362191\pi$
$281$	0.226991	+	1.43316i	0.0135411	+	0.0854954i	−0.979992	+	0.199036i	$0.936219\pi$
$282$		0			0
$283$	−2.91195	−	8.96207i	−0.173098	−	0.532740i	0.826444	−	0.563019i	$-0.190360\pi$
$283$	−2.91195	−	8.96207i	−0.173098	−	0.532740i	−0.999541	+	0.0302793i	$0.990360\pi$
$284$	−2.84802	+	2.84802i	−0.168999	+	0.168999i
$285$		0			0
$286$	1.81287			0.107197
$287$	5.19940	−	8.92345i	0.306911	−	0.526734i
$288$		0			0
$289$	−9.33448	+	12.8478i	−0.549087	+	0.755753i
$290$	−27.2487	+	27.2487i	−1.60010	+	1.60010i
$291$		0			0
$292$	−10.8881	+	3.53775i	−0.637176	+	0.207031i
$293$	−0.169720	−	1.07157i	−0.00991512	−	0.0626016i	0.982235	−	0.187657i	$-0.0600892\pi$
$293$	−0.169720	−	1.07157i	−0.00991512	−	0.0626016i	−0.992150	+	0.125055i	$0.960089\pi$
$294$		0			0
$295$	21.0776	+	6.84853i	1.22719	+	0.398737i
$296$		−	11.0029i		−	0.639533i
$297$		0			0
$298$	10.0619	+	19.7476i	0.582871	+	1.14395i
$299$	2.56108	+	1.30494i	0.148111	+	0.0754665i
$300$		0			0
$301$	−12.0656	−	12.0656i	−0.695450	−	0.695450i
$302$	−1.08660	+	2.13256i	−0.0625266	+	0.122715i
$303$		0			0
$304$	−0.572268	+	0.291585i	−0.0328218	+	0.0167236i
$305$	−5.77176	−	4.19343i	−0.330490	−	0.240115i
$306$		0			0
$307$	17.4258	+	23.9845i	0.994542	+	1.36887i	0.928615	+	0.371045i	$0.121000\pi$
$307$	17.4258	+	23.9845i	0.994542	+	1.36887i	0.0659270	+	0.997824i	$0.479000\pi$
$308$	−0.616692	−	0.848803i	−0.0351393	−	0.0483650i
$309$		0			0
$310$	−4.53691	−	3.29626i	−0.257679	−	0.187215i
$311$	15.3673	−	7.83002i	0.871399	−	0.444000i	0.0396900	−	0.999212i	$-0.487363\pi$
$311$	15.3673	−	7.83002i	0.871399	−	0.444000i	0.831709	+	0.555212i	$0.187363\pi$
$312$		0			0
$313$	−0.736533	+	1.44553i	−0.0416313	+	0.0817060i	−0.910885	−	0.412660i	$-0.864600\pi$
$313$	−0.736533	+	1.44553i	−0.0416313	+	0.0817060i	0.869254	+	0.494366i	$0.164600\pi$
$314$	−21.2871	−	21.2871i	−1.20130	−	1.20130i
$315$		0			0
$316$	9.63078	+	4.90713i	0.541774	+	0.276048i
$317$	7.39686	+	14.5172i	0.415449	+	0.815364i	0.999992	+	0.00400175i	$0.00127380\pi$
$317$	7.39686	+	14.5172i	0.415449	+	0.815364i	−0.584543	+	0.811363i	$0.698726\pi$
$318$		0			0
$319$			5.74899i			0.321882i
$320$	3.98764	+	1.29566i	0.222916	+	0.0724298i
$321$		0			0
$322$	−0.814664	−	5.14359i	−0.0453995	−	0.286641i
$323$	0.129343	−	0.0420260i	0.00719682	−	0.00233839i
$324$		0			0
$325$	−2.52657	+	2.52657i	−0.140149	+	0.140149i
$326$	17.7424	−	24.4203i	0.982660	−	1.35251i
$327$		0			0
$328$	−9.02395	−	7.36708i	−0.498264	−	0.406779i
$329$	−10.2261			−0.563786
$330$		0			0
$331$	−17.9285	+	17.9285i	−0.985441	+	0.985441i	−0.999896	−	0.0144544i	$-0.995399\pi$
$331$	−17.9285	+	17.9285i	−0.985441	+	0.985441i	0.0144544	+	0.999896i	$0.495399\pi$
$332$	1.88290	+	5.79496i	0.103337	+	0.318040i
$333$		0			0
$334$	−0.744460	−	4.70034i	−0.0407350	−	0.257191i
$335$	−3.59856	+	22.7204i	−0.196610	+	1.24135i
$336$		0			0
$337$		−	26.2434i		−	1.42957i	−0.699344	−	0.714785i	$-0.746525\pi$
$337$		−	26.2434i		−	1.42957i	0.699344	−	0.714785i	$-0.253475\pi$
$338$	−5.65282	+	17.3976i	−0.307473	+	0.946305i
$339$		0			0
$340$	2.39755	+	1.22161i	0.130025	+	0.0662513i
$341$	−0.826331	+	0.130878i	−0.0447483	+	0.00708744i
$342$		0			0
$343$	−8.34654	+	16.3810i	−0.450671	+	0.884491i
$344$	−15.5710	+	11.3130i	−0.839532	+	0.609956i
$345$		0			0
$346$	−16.2398	−	11.7989i	−0.873055	−	0.634311i
$347$	16.4622	+	2.60735i	0.883735	+	0.139970i	0.581774	−	0.813351i	$-0.302359\pi$
$347$	16.4622	+	2.60735i	0.883735	+	0.139970i	0.301961	+	0.953320i	$0.402359\pi$
$348$		0			0
$349$	5.08471	+	6.99851i	0.272178	+	0.374622i	0.923124	−	0.384503i	$-0.125627\pi$
$349$	5.08471	+	6.99851i	0.272178	+	0.374622i	−0.650945	+	0.759125i	$0.725627\pi$
$350$	6.39396	+	1.01270i	0.341772	+	0.0541313i
$351$		0			0
$352$	−3.04158	+	1.54976i	−0.162117	+	0.0826027i
$353$	11.1586	−	8.10719i	0.593912	−	0.431502i	−0.249801	−	0.968297i	$-0.580365\pi$
$353$	11.1586	−	8.10719i	0.593912	−	0.431502i	0.843713	+	0.536795i	$0.180365\pi$
$354$		0			0
$355$	−8.22035	−	8.22035i	−0.436291	−	0.436291i
$356$	2.67379	−	0.423486i	0.141710	−	0.0224447i
$357$		0			0
$358$	3.31045	+	6.49712i	0.174962	+	0.343383i
$359$	5.59785	−	17.2284i	0.295443	−	0.909281i	−0.687629	−	0.726062i	$-0.741348\pi$
$359$	5.59785	−	17.2284i	0.295443	−	0.909281i	0.983072	−	0.183219i	$-0.0586517\pi$
$360$		0			0
$361$	−18.0544	−	5.86622i	−0.950229	−	0.308748i
$362$	1.24330	−	7.84987i	0.0653462	−	0.412580i
$363$		0			0
$364$	−2.19759	+	0.714040i	−0.115185	+	0.0374258i
$365$	−10.2111	−	31.4267i	−0.534476	−	1.64495i
$366$		0			0
$367$	13.5735	−	18.6823i	0.708531	−	0.975210i	−0.291296	−	0.956633i	$-0.594087\pi$
$367$	13.5735	−	18.6823i	0.708531	−	0.975210i	0.999827	−	0.0185766i	$-0.00591347\pi$
$368$	−9.41019			−0.490540
$369$		0			0
$370$	−28.0911			−1.46038
$371$	−11.8414	+	16.2983i	−0.614774	+	0.846164i
$372$		0			0
$373$	4.36956	+	13.4481i	0.226247	+	0.696317i	0.998163	+	0.0605920i	$0.0192989\pi$
$373$	4.36956	+	13.4481i	0.226247	+	0.696317i	−0.771915	+	0.635725i	$0.780701\pi$
$374$	1.19521	−	0.388348i	0.0618029	−	0.0200810i
$375$		0			0
$376$	−1.80443	+	11.3927i	−0.0930561	+	0.587533i
$377$	12.0417	+	3.91259i	0.620180	+	0.201509i
$378$		0			0
$379$	−11.4876	+	35.3552i	−0.590079	+	1.81608i	−0.0122385	+	0.999925i	$0.503896\pi$
$379$	−11.4876	+	35.3552i	−0.590079	+	1.81608i	−0.577840	+	0.816150i	$0.696104\pi$
$380$	0.148439	+	0.291328i	0.00761475	+	0.0149448i
$381$		0			0
$382$	−37.8741	+	5.99867i	−1.93781	+	0.306919i
$383$	4.89444	+	4.89444i	0.250094	+	0.250094i	0.821009	−	0.570915i	$-0.193411\pi$
$383$	4.89444	+	4.89444i	0.250094	+	0.250094i	−0.570915	+	0.821009i	$0.693411\pi$
$384$		0			0
$385$	2.44993	−	1.77998i	0.124860	−	0.0907162i
$386$	22.2607	−	11.3424i	1.13304	−	0.577314i
$387$		0			0
$388$	−1.12096	−	0.177542i	−0.0569079	−	0.00901333i
$389$	−1.39142	−	1.91513i	−0.0705480	−	0.0971010i	0.772285	−	0.635276i	$-0.219114\pi$
$389$	−1.39142	−	1.91513i	−0.0705480	−	0.0971010i	−0.842833	+	0.538175i	$0.819114\pi$
$390$		0			0
$391$	1.96805	+	0.311708i	0.0995284	+	0.0157637i
$392$	6.47394	+	4.70359i	0.326983	+	0.237567i
$393$		0			0
$394$	−1.29056	+	0.937648i	−0.0650176	+	0.0472380i
$395$	−14.1636	+	27.7977i	−0.712650	+	1.39865i
$396$		0			0
$397$	15.9514	−	2.52646i	0.800580	−	0.126799i	0.257278	−	0.966337i	$-0.417174\pi$
$397$	15.9514	−	2.52646i	0.800580	−	0.126799i	0.543301	+	0.839538i	$0.317174\pi$
$398$	0.629676	+	0.320836i	0.0315628	+	0.0160820i
$399$		0			0
$400$	3.61480	−	11.1252i	0.180740	−	0.556261i
$401$		−	4.77242i		−	0.238323i	−0.992875	−	0.119162i	$-0.961979\pi$
$401$		−	4.77242i		−	0.238323i	0.992875	−	0.119162i	$-0.0380207\pi$
$402$		0			0
$403$	−0.288242	+	1.81989i	−0.0143584	+	0.0906551i
$404$	−0.778554	−	4.91560i	−0.0387345	−	0.244560i
$405$		0			0
$406$	−7.08872	−	21.8168i	−0.351807	−	1.08275i
$407$	−2.96336	+	2.96336i	−0.146888	+	0.146888i
$408$		0			0
$409$	−9.57331			−0.473370			−0.236685	−	0.971586i	$-0.576061\pi$
$409$	−9.57331			−0.473370			−0.236685	+	0.971586i	$0.576061\pi$
$410$	−18.8085	+	23.0386i	−0.928887	+	1.13780i
$411$		0			0
$412$	7.65665	−	10.5385i	0.377216	−	0.519194i
$413$	−9.32879	+	9.32879i	−0.459040	+	0.459040i
$414$		0			0
$415$	−16.7262	+	5.43468i	−0.821058	+	0.266778i
$416$	1.17609	+	7.42556i	0.0576627	+	0.364068i
$417$		0			0
$418$	0.145231	+	0.0471883i	0.00710347	+	0.00230806i
$419$			8.06247i			0.393878i	0.980416	+	0.196939i	$0.0631000\pi$
$419$			8.06247i			0.393878i	−0.980416	+	0.196939i	$0.936900\pi$
$420$		0			0
$421$	−8.01644	−	15.7331i	−0.390697	−	0.766787i	0.608954	−	0.793206i	$-0.291590\pi$
$421$	−8.01644	−	15.7331i	−0.390697	−	0.766787i	−0.999651	+	0.0264191i	$0.991590\pi$
$422$	−34.2500	−	17.4512i	−1.66726	−	0.849513i
$423$		0			0
$424$	16.0681	+	16.0681i	0.780334	+	0.780334i
$425$	−1.12452	+	2.20699i	−0.0545471	+	0.107055i
$426$		0			0
$427$	3.78405	−	1.92807i	0.183123	−	0.0933058i
$428$	−7.24011	−	5.26025i	−0.349964	−	0.254264i
$429$		0			0
$430$	28.8827	+	39.7536i	1.39285	+	1.91709i
$431$	5.96805	+	8.21431i	0.287471	+	0.395670i	0.928191	−	0.372105i	$-0.121364\pi$
$431$	5.96805	+	8.21431i	0.287471	+	0.395670i	−0.640720	+	0.767775i	$0.721364\pi$
$432$		0			0
$433$	26.8766	+	19.5270i	1.29161	+	0.938406i	0.999837	−	0.0180823i	$-0.00575610\pi$
$433$	26.8766	+	19.5270i	1.29161	+	0.938406i	0.291769	+	0.956489i	$0.405756\pi$
$434$	2.97446	−	1.51557i	0.142779	−	0.0727495i
$435$		0			0
$436$	−1.00428	+	1.97101i	−0.0480962	+	0.0943941i
$437$	0.171204	+	0.171204i	0.00818981	+	0.00818981i
$438$		0			0
$439$	−32.8349	−	16.7302i	−1.56713	−	0.798490i	−0.567436	−	0.823418i	$-0.692065\pi$
$439$	−32.8349	−	16.7302i	−1.56713	−	0.798490i	−0.999689	+	0.0249274i	$0.992065\pi$
$440$	−1.55074	−	3.04349i	−0.0739285	−	0.145093i
$441$		0			0
$442$		−	2.76776i		−	0.131649i
$443$	−29.3333	−	9.53097i	−1.39367	−	0.452830i	−0.486530	−	0.873664i	$-0.661738\pi$
$443$	−29.3333	−	9.53097i	−1.39367	−	0.452830i	−0.907138	+	0.420834i	$0.861738\pi$
$444$		0			0
$445$	1.22232	+	7.71745i	0.0579437	+	0.365842i
$446$	6.64563	−	2.15930i	0.314680	−	0.102246i
$447$		0			0
$448$	−1.76490	+	1.76490i	−0.0833837	+	0.0833837i
$449$	−17.4190	+	23.9753i	−0.822055	+	1.13146i	0.167295	+	0.985907i	$0.446497\pi$
$449$	−17.4190	+	23.9753i	−0.822055	+	1.13146i	−0.989350	+	0.145555i	$0.953503\pi$
$450$		0			0
$451$	0.446235	+	4.41451i	0.0210124	+	0.207871i
$452$	−7.20681			−0.338980
$453$		0			0
$454$	26.1743	−	26.1743i	1.22842	−	1.22842i
$455$	−2.06096	−	6.34298i	−0.0966193	−	0.297364i
$456$		0			0
$457$	−1.18792	−	7.50026i	−0.0555688	−	0.350847i	−0.999769	−	0.0214764i	$-0.993163\pi$
$457$	−1.18792	−	7.50026i	−0.0555688	−	0.350847i	0.944201	−	0.329371i	$-0.106837\pi$
$458$	2.65689	−	16.7750i	0.124149	−	0.783843i
$459$		0			0
$460$			4.79050i			0.223358i
$461$	7.81323	−	24.0467i	0.363898	−	1.11996i	−0.586770	−	0.809754i	$-0.699601\pi$
$461$	7.81323	−	24.0467i	0.363898	−	1.11996i	0.950668	−	0.310210i	$-0.100399\pi$
$462$		0			0
$463$	13.1377	+	6.69397i	0.610559	+	0.311095i	0.731791	−	0.681529i	$-0.238685\pi$
$463$	13.1377	+	6.69397i	0.610559	+	0.311095i	−0.121233	+	0.992624i	$0.538685\pi$
$464$	−40.9409	+	6.48440i	−1.90063	+	0.301031i
$465$		0			0
$466$	1.00134	−	1.96523i	0.0463860	−	0.0910376i
$467$	−17.8981	+	13.0037i	−0.828226	+	0.601742i	−0.919057	−	0.394125i	$-0.871048\pi$
$467$	−17.8981	+	13.0037i	−0.828226	+	0.601742i	0.0908306	+	0.995866i	$0.471048\pi$
$468$		0			0
$469$	−11.0784	−	8.04896i	−0.511555	−	0.371667i
$470$	29.0861	+	4.60679i	1.34164	+	0.212495i
$471$		0			0
$472$	8.74689	+	12.0391i	0.402608	+	0.554143i
$473$	7.24052	+	1.14679i	0.332920	+	0.0527293i
$474$		0			0
$475$	−0.268172	+	0.136641i	−0.0123046	+	0.00626950i
$476$	−1.29590	+	0.941523i	−0.0593973	+	0.0431546i
$477$		0			0
$478$	−8.60238	−	8.60238i	−0.393464	−	0.393464i
$479$	15.6892	−	2.48493i	0.716859	−	0.113539i	0.212660	−	0.977126i	$-0.431787\pi$
$479$	15.6892	−	2.48493i	0.716859	−	0.113539i	0.504200	+	0.863587i	$0.331787\pi$
$480$		0			0
$481$	4.19022	+	8.22377i	0.191058	+	0.374972i
$482$	5.71468	−	17.5880i	0.260297	−	0.801110i
$483$		0			0
$484$	−9.39192	−	3.05162i	−0.426905	−	0.138710i
$485$	0.512446	−	3.23546i	0.0232690	−	0.146915i
$486$		0			0
$487$	20.0083	−	6.50110i	0.906664	−	0.294593i	0.181679	−	0.983358i	$-0.441847\pi$
$487$	20.0083	−	6.50110i	0.906664	−	0.294593i	0.724985	+	0.688765i	$0.241847\pi$
$488$	−1.48031	−	4.55593i	−0.0670105	−	0.206237i
$489$		0			0
$490$	12.0085	−	16.5283i	0.542489	−	0.746673i
$491$	0.0541126			0.00244207			0.00122103	−	0.999999i	$-0.499611\pi$
$491$	0.0541126			0.00244207			0.00122103	+	0.999999i	$0.499611\pi$
$492$		0			0
$493$	8.77717			0.395304
$494$	0.197680	−	0.272083i	0.00889402	−	0.0122416i
$495$		0			0
$496$	−1.86407	−	5.73702i	−0.0836992	−	0.257600i
$497$	6.58168	−	2.13852i	0.295229	−	0.0959256i
$498$		0			0
$499$	5.08470	−	32.1035i	0.227623	−	1.43715i	−0.563815	−	0.825901i	$-0.690667\pi$
$499$	5.08470	−	32.1035i	0.227623	−	1.43715i	0.791437	−	0.611251i	$-0.209333\pi$
$500$	6.43133	+	2.08966i	0.287618	+	0.0934526i
$501$		0			0
$502$	−2.98001	+	9.17151i	−0.133004	+	0.409345i
$503$	14.6571	+	28.7662i	0.653529	+	1.28262i	0.945321	+	0.326140i	$0.105748\pi$
$503$	14.6571	+	28.7662i	0.653529	+	1.28262i	−0.291793	+	0.956482i	$0.594252\pi$
$504$		0			0
$505$	14.1881	−	2.24717i	0.631362	−	0.0999979i
$506$	1.58204	+	1.58204i	0.0703302	+	0.0703302i
$507$		0			0
$508$	−4.73284	+	3.43861i	−0.209986	+	0.152564i
$509$	25.7195	−	13.1047i	1.14000	−	0.580857i	0.221059	−	0.975260i	$-0.429049\pi$
$509$	25.7195	−	13.1047i	1.14000	−	0.580857i	0.918938	+	0.394403i	$0.129049\pi$
$510$		0			0
$511$	19.4284	+	3.07716i	0.859462	+	0.136125i
$512$	−3.78156	−	5.20487i	−0.167123	−	0.230025i
$513$		0			0
$514$	37.2232	+	5.89558i	1.64185	+	0.260043i
$515$	30.4176	+	22.0997i	1.34036	+	0.973829i
$516$		0			0
$517$	3.55431	−	2.58236i	0.156318	−	0.113572i
$518$	7.59172	−	14.8996i	0.333561	−	0.654650i
$519$		0			0
$520$	−7.43022	+	1.17683i	−0.325837	+	0.0516075i
$521$	−15.6014	−	7.94931i	−0.683509	−	0.348265i	0.0775127	−	0.996991i	$-0.475302\pi$
$521$	−15.6014	−	7.94931i	−0.683509	−	0.348265i	−0.761022	+	0.648726i	$0.775302\pi$
$522$		0			0
$523$	2.25075	−	6.92710i	0.0984185	−	0.302901i	−0.889711	−	0.456524i	$-0.849094\pi$
$523$	2.25075	−	6.92710i	0.0984185	−	0.302901i	0.988130	+	0.153623i	$0.0490942\pi$
$524$			0.680896i			0.0297451i
$525$		0			0
$526$	−1.57178	+	9.92380i	−0.0685327	+	0.432698i
$527$	0.199816	+	1.26159i	0.00870411	+	0.0549556i
$528$		0			0
$529$	−6.01119	−	18.5005i	−0.261356	−	0.804371i
$530$	41.0226	−	41.0226i	1.78191	−	1.78191i
$531$		0			0
$532$	−0.194637			−0.00843860
$533$	9.55023	+	2.06971i	0.413667	+	0.0896491i
$534$		0			0
$535$	15.1829	−	20.8974i	0.656413	−	0.903474i
$536$	−10.9220	+	10.9220i	−0.471757	+	0.471757i
$537$		0			0
$538$	22.3853	−	7.27343i	0.965100	−	0.313580i
$539$	−0.476798	−	3.01039i	−0.0205372	−	0.129667i
$540$		0			0
$541$	−28.9790	−	9.41585i	−1.24590	−	0.404819i	−0.389453	−	0.921046i	$-0.627336\pi$
$541$	−28.9790	−	9.41585i	−1.24590	−	0.404819i	−0.856451	+	0.516228i	$0.827336\pi$
$542$		−	27.2790i		−	1.17173i
$543$		0			0
$544$	2.36608	+	4.64368i	0.101445	+	0.199096i
$545$	−5.68900	−	2.89869i	−0.243690	−	0.124166i
$546$		0			0
$547$	−22.9755	−	22.9755i	−0.982360	−	0.982360i	0.0174867	−	0.999847i	$-0.494434\pi$
$547$	−22.9755	−	22.9755i	−0.982360	−	0.982360i	−0.999847	+	0.0174867i	$0.994434\pi$
$548$	−7.95254	+	15.6077i	−0.339716	+	0.666729i
$549$		0			0
$550$	−2.47809	+	1.26265i	−0.105666	+	0.0538395i
$551$	0.862832	+	0.626884i	0.0367579	+	0.0267062i
$552$		0			0
$553$	−10.9162	−	15.0249i	−0.464205	−	0.638923i
$554$	19.3427	+	26.6230i	0.821793	+	1.13110i
$555$		0			0
$556$	4.81727	+	3.49995i	0.204298	+	0.148431i
$557$	22.1309	−	11.2762i	0.937716	−	0.477790i	0.0828053	−	0.996566i	$-0.473612\pi$
$557$	22.1309	−	11.2762i	0.937716	−	0.477790i	0.854910	+	0.518776i	$0.173612\pi$
$558$		0			0
$559$	7.32972	−	14.3854i	0.310014	−	0.608437i
$560$	15.4393	+	15.4393i	0.652429	+	0.652429i
$561$		0			0
$562$	2.21634	+	1.12928i	0.0934907	+	0.0476359i
$563$	−11.3113	−	22.1997i	−0.476716	−	0.935608i	−0.996680	−	0.0814196i	$-0.974055\pi$
$563$	−11.3113	−	22.1997i	−0.476716	−	0.935608i	0.519964	−	0.854188i	$-0.325945\pi$
$564$		0			0
$565$		−	20.8013i		−	0.875118i
$566$	−15.3634	−	4.99188i	−0.645773	−	0.209824i
$567$		0			0
$568$	−1.22112	−	7.70983i	−0.0512370	−	0.323497i
$569$	13.3652	−	4.34260i	0.560297	−	0.182051i	−0.0151580	−	0.999885i	$-0.504825\pi$
$569$	13.3652	−	4.34260i	0.560297	−	0.182051i	0.575455	+	0.817834i	$0.304825\pi$
$570$		0			0
$571$	−21.7176	+	21.7176i	−0.908854	+	0.908854i	−0.996180	−	0.0873260i	$-0.972168\pi$
$571$	−21.7176	+	21.7176i	−0.908854	+	0.908854i	0.0873260	+	0.996180i	$0.472168\pi$
$572$	0.583505	−	0.803126i	0.0243976	−	0.0335804i
$573$		0			0
$574$	−7.13667	−	16.2024i	−0.297879	−	0.676274i
$575$	−4.40974			−0.183899
$576$		0			0
$577$	0.105596	−	0.105596i	0.00439603	−	0.00439603i	−0.704905	−	0.709301i	$-0.749011\pi$
$577$	0.105596	−	0.105596i	0.00439603	−	0.00439603i	0.709301	+	0.704905i	$0.249011\pi$
$578$	8.41266	+	25.8915i	0.349921	+	1.07694i
$579$		0			0
$580$	3.30105	+	20.8420i	0.137069	+	0.865418i
$581$	1.63776	−	10.3404i	0.0679456	−	0.428992i
$582$		0			0
$583$		−	8.65505i		−	0.358456i
$584$	6.85637	−	21.1017i	0.283719	−	0.873196i
$585$		0			0
$586$	−1.65714	−	0.844356i	−0.0684559	−	0.0348800i
$587$	−15.8079	+	2.50372i	−0.652460	+	0.103339i	−0.473885	−	0.880587i	$-0.657149\pi$
$587$	−15.8079	+	2.50372i	−0.652460	+	0.103339i	−0.178575	+	0.983926i	$0.557149\pi$
$588$		0			0
$589$	−0.0704625	+	0.138290i	−0.00290335	+	0.00569815i
$590$	30.7363	−	22.3313i	1.26540	−	0.919363i
$591$		0			0
$592$	−24.4457	−	17.7609i	−1.00471	−	0.729967i
$593$	−1.94396	−	0.307893i	−0.0798289	−	0.0126436i	0.116392	−	0.993203i	$-0.462867\pi$
$593$	−1.94396	−	0.307893i	−0.0798289	−	0.0126436i	−0.196221	+	0.980560i	$0.562867\pi$
$594$		0			0
$595$	−2.71756	−	3.74039i	−0.111409	−	0.153341i
$596$	11.9871	+	1.89857i	0.491010	+	0.0777683i
$597$		0			0
$598$	4.39039	−	2.23702i	0.179537	−	0.0914785i
$599$	−15.0623	+	10.9434i	−0.615429	+	0.447136i	−0.851322	−	0.524644i	$-0.824199\pi$
$599$	−15.0623	+	10.9434i	−0.615429	+	0.447136i	0.235893	+	0.971779i	$0.424199\pi$
$600$		0			0
$601$	7.07160	+	7.07160i	0.288456	+	0.288456i	0.836470	−	0.548013i	$-0.184616\pi$
$601$	7.07160	+	7.07160i	0.288456	+	0.288456i	−0.548013	+	0.836470i	$0.684616\pi$
$602$	−28.8911	+	4.57590i	−1.17751	+	0.186500i
$603$		0			0
$604$	0.595015	+	1.16778i	0.0242108	+	0.0475164i
$605$	8.80801	−	27.1083i	0.358096	−	1.10211i
$606$		0			0
$607$	36.0725	+	11.7207i	1.46414	+	0.475727i	0.929331	−	0.369248i	$-0.120385\pi$
$607$	36.0725	+	11.7207i	1.46414	+	0.475727i	0.534806	+	0.844975i	$0.320385\pi$
$608$	−0.0990668	+	0.625483i	−0.00401769	+	0.0253667i
$609$		0			0
$610$	−11.6315	+	3.77931i	−0.470946	+	0.153020i
$611$	−2.99000	−	9.20226i	−0.120962	−	0.372284i
$612$		0			0
$613$	−15.8786	+	21.8550i	−0.641331	+	0.882717i	−0.998686	−	0.0512520i	$-0.983679\pi$
$613$	−15.8786	+	21.8550i	−0.641331	+	0.882717i	0.357354	+	0.933969i	$0.383679\pi$
$614$	50.8222			2.05102
$615$		0			0
$616$	2.03337			0.0819269
$617$	5.89230	−	8.11005i	0.237215	−	0.326498i	−0.673768	−	0.738943i	$-0.735325\pi$
$617$	5.89230	−	8.11005i	0.237215	−	0.326498i	0.910983	+	0.412445i	$0.135325\pi$
$618$		0			0
$619$	10.2987	+	31.6960i	0.413938	+	1.27397i	0.913197	+	0.407518i	$0.133606\pi$
$619$	10.2987	+	31.6960i	0.413938	+	1.27397i	−0.499259	+	0.866453i	$0.666394\pi$
$620$	−2.92058	+	0.948953i	−0.117293	+	0.0381109i
$621$		0			0
$622$	4.62518	−	29.2022i	0.185453	−	1.17090i
$623$	−4.42370	−	1.43735i	−0.177232	−	0.0575861i
$624$		0			0
$625$	−9.64900	+	29.6966i	−0.385960	+	1.18786i
$626$	1.26262	+	2.47803i	0.0504643	+	0.0990418i
$627$		0			0
$628$	−16.2821	+	2.57883i	−0.649727	+	0.102907i
$629$	4.52426	+	4.52426i	0.180394	+	0.180394i
$630$		0			0
$631$	8.52090	−	6.19080i	0.339212	−	0.246452i	−0.405117	−	0.914265i	$-0.632769\pi$
$631$	8.52090	−	6.19080i	0.339212	−	0.246452i	0.744329	+	0.667813i	$0.232769\pi$
$632$	−18.6650	+	9.51032i	−0.742456	+	0.378300i
$633$		0			0
$634$	27.5867	+	4.36931i	1.09561	+	0.173527i
$635$	−9.92500	−	13.6606i	−0.393862	−	0.542104i
$636$		0			0
$637$	−6.62999	−	1.05009i	−0.262690	−	0.0416060i
$638$	7.97313	+	5.79282i	0.315659	+	0.229340i
$639$		0			0
$640$	27.4121	−	19.9160i	1.08356	−	0.787250i
$641$	2.10778	−	4.13674i	0.0832521	−	0.163391i	−0.845627	−	0.533774i	$-0.820773\pi$
$641$	2.10778	−	4.13674i	0.0832521	−	0.163391i	0.928879	+	0.370382i	$0.120773\pi$
$642$		0			0
$643$	−29.6739	+	4.69989i	−1.17023	+	0.185346i	−0.711143	−	0.703048i	$-0.751822\pi$
$643$	−29.6739	+	4.69989i	−1.17023	+	0.185346i	−0.459083	+	0.888393i	$0.651822\pi$
$644$	−2.54090	−	1.29465i	−0.100125	−	0.0510164i
$645$		0			0
$646$	0.0720440	−	0.221729i	0.00283453	−	0.00872379i
$647$		−	16.4853i		−	0.648104i	−0.946039	−	0.324052i	$-0.894955\pi$
$647$		−	16.4853i		−	0.648104i	0.946039	−	0.324052i	$-0.105045\pi$
$648$		0			0
$649$	0.886663	−	5.59817i	0.0348046	−	0.219747i
$650$	0.958206	+	6.04988i	0.0375839	+	0.237296i
$651$		0			0
$652$	−5.10782	−	15.7202i	−0.200038	−	0.615652i
$653$	−23.6145	+	23.6145i	−0.924105	+	0.924105i	−0.997316	−	0.0732110i	$-0.976675\pi$
$653$	−23.6145	+	23.6145i	−0.924105	+	0.924105i	0.0732110	+	0.997316i	$0.476675\pi$
$654$		0			0
$655$	−1.96530			−0.0767905
$656$	−30.9342	+	8.15703i	−1.20778	+	0.318478i
$657$		0			0
$658$	−10.3041	+	14.1824i	−0.401696	+	0.552887i
$659$	3.37421	−	3.37421i	0.131441	−	0.131441i	−0.638326	−	0.769766i	$-0.720373\pi$
$659$	3.37421	−	3.37421i	0.131441	−	0.131441i	0.769766	+	0.638326i	$0.220373\pi$
$660$		0			0
$661$	12.2982	−	3.99593i	0.478345	−	0.155424i	−0.0599133	−	0.998204i	$-0.519082\pi$
$661$	12.2982	−	3.99593i	0.478345	−	0.155424i	0.538258	+	0.842780i	$0.319082\pi$
$662$	6.79942	+	42.9298i	0.264267	+	1.66852i
$663$		0			0
$664$	−11.2310	−	3.64917i	−0.435847	−	0.141615i
$665$		−	0.561789i		−	0.0217853i
$666$		0			0
$667$	7.09406	+	13.9229i	0.274683	+	0.539096i
$668$	−2.32193	−	1.18308i	−0.0898383	−	0.0457749i
$669$		0			0
$670$	27.8843	+	27.8843i	1.07727	+	1.07727i
$671$	−0.828340	+	1.62571i	−0.0319777	+	0.0627598i
$672$		0			0
$673$	5.66568	−	2.88681i	0.218396	−	0.111278i	−0.341370	−	0.939929i	$-0.610891\pi$
$673$	5.66568	−	2.88681i	0.218396	−	0.111278i	0.559766	+	0.828651i	$0.310891\pi$
$674$	−36.3963	−	26.4435i	−1.40193	−	1.01856i
$675$		0			0
$676$	5.88791	+	8.10402i	0.226458	+	0.311693i
$677$	20.5198	+	28.2431i	0.788642	+	1.08547i	0.994276	+	0.106843i	$0.0340743\pi$
$677$	20.5198	+	28.2431i	0.788642	+	1.08547i	−0.205634	+	0.978629i	$0.565926\pi$
$678$		0			0
$679$	1.57761	+	1.14620i	0.0605430	+	0.0439871i
$680$	−4.64660	+	2.36756i	−0.178189	+	0.0907918i
$681$		0			0
$682$	−0.651119	+	1.27789i	−0.0249326	+	0.0489331i
$683$	−17.6969	−	17.6969i	−0.677154	−	0.677154i	0.282201	−	0.959355i	$-0.408935\pi$
$683$	−17.6969	−	17.6969i	−0.677154	−	0.677154i	−0.959355	+	0.282201i	$0.908935\pi$
$684$		0			0
$685$	−45.0492	−	22.9537i	−1.72124	−	0.877017i
$686$	14.3082	+	28.0815i	0.546291	+	1.07216i
$687$		0			0
$688$			52.8562i			2.01512i
$689$	−18.1287	−	5.89037i	−0.690649	−	0.224405i
$690$		0			0
$691$	4.16500	+	26.2968i	0.158444	+	1.00038i	0.930891	+	0.365298i	$0.119033\pi$
$691$	4.16500	+	26.2968i	0.158444	+	1.00038i	−0.772446	+	0.635080i	$0.780967\pi$
$692$	−10.4541	+	3.39675i	−0.397406	+	0.129125i
$693$		0			0
$694$	20.2037	−	20.2037i	0.766923	−	0.766923i
$695$	−10.1020	+	13.9043i	−0.383192	+	0.527419i
$696$		0			0
$697$	6.73977	−	0.681281i	0.255287	−	0.0258053i
$698$	14.8295			0.561306
$699$		0			0
$700$	2.50666	−	2.50666i	0.0947427	−	0.0947427i
$701$	−6.42667	−	19.7793i	−0.242732	−	0.747052i	−0.996001	−	0.0893399i	$-0.971524\pi$
$701$	−6.42667	−	19.7793i	−0.242732	−	0.747052i	0.753269	−	0.657712i	$-0.228476\pi$
$702$		0			0
$703$	0.121621	+	0.767886i	0.00458703	+	0.0289614i
$704$	0.167746	−	1.05911i	0.00632218	−	0.0399167i
$705$		0			0
$706$		−	23.6446i		−	0.889874i
$707$	−2.64248	+	8.13272i	−0.0993807	+	0.305862i
$708$		0			0
$709$	7.83436	+	3.99181i	0.294226	+	0.149915i	0.594872	−	0.803820i	$-0.297203\pi$
$709$	7.83436	+	3.99181i	0.294226	+	0.149915i	−0.300647	+	0.953736i	$0.597203\pi$
$710$	−19.6836	+	3.11758i	−0.738712	+	0.117001i
$711$		0			0
$712$	−2.38188	+	4.67471i	−0.0892649	+	0.175192i
$713$	−1.83971	+	1.33662i	−0.0688975	+	0.0500570i
$714$		0			0
$715$	2.31809	+	1.68419i	0.0866918	+	0.0629852i
$716$	3.94384	+	0.624643i	0.147388	+	0.0233440i
$717$		0			0
$718$	−18.2531	−	25.1233i	−0.681201	−	0.937593i
$719$	−12.8945	−	2.04229i	−0.480885	−	0.0761647i	−0.0887143	−	0.996057i	$-0.528276\pi$
$719$	−12.8945	−	2.04229i	−0.480885	−	0.0761647i	−0.392171	+	0.919892i	$0.628276\pi$
$720$		0			0
$721$	−19.9422	+	10.1611i	−0.742688	+	0.378418i
$722$	−26.3277	+	19.1282i	−0.979816	+	0.711878i
$723$		0			0
$724$	−3.07742	−	3.07742i	−0.114371	−	0.114371i
$725$	−19.1855	+	3.03868i	−0.712530	+	0.112854i
$726$		0			0
$727$	−12.5723	−	24.6746i	−0.466282	−	0.915131i	−0.997685	−	0.0680111i	$-0.978335\pi$
$727$	−12.5723	−	24.6746i	−0.466282	−	0.915131i	0.531402	−	0.847120i	$-0.321665\pi$
$728$	1.38385	−	4.25906i	0.0512890	−	0.157851i
$729$		0			0
$730$	−53.8738	−	17.5047i	−1.99396	−	0.647877i
$731$	1.75084	−	11.0543i	0.0647570	−	0.408860i
$732$		0			0
$733$	−23.2536	+	7.55554i	−0.858890	+	0.279070i	−0.705165	−	0.709043i	$-0.749127\pi$
$733$	−23.2536	+	7.55554i	−0.858890	+	0.279070i	−0.153725	+	0.988114i	$0.549127\pi$
$734$	−12.2331	−	37.6495i	−0.451531	−	1.38967i
$735$		0			0
$736$	−5.45374	+	7.50643i	−0.201027	+	0.276690i
$737$	5.88311			0.216707
$738$		0			0
$739$	−35.1342			−1.29243			−0.646215	−	0.763155i	$-0.723649\pi$
$739$	−35.1342			−1.29243			−0.646215	+	0.763155i	$0.723649\pi$
$740$	−9.04162	+	12.4447i	−0.332377	+	0.457477i
$741$		0			0
$742$	10.6720	+	32.8450i	0.391782	+	1.20578i
$743$	−5.44093	+	1.76787i	−0.199608	+	0.0648567i	−0.407115	−	0.913377i	$-0.633465\pi$
$743$	−5.44093	+	1.76787i	−0.199608	+	0.0648567i	0.207507	+	0.978234i	$0.433465\pi$
$744$		0			0
$745$	−5.47991	+	34.5988i	−0.200768	+	1.26760i
$746$	23.0537	+	7.49061i	0.844057	+	0.274251i
$747$		0			0
$748$	0.212657	−	0.654492i	0.00777552	−	0.0239306i
$749$	6.98083	+	13.7007i	0.255074	+	0.500611i
$750$		0			0
$751$	−11.5290	+	1.82601i	−0.420699	+	0.0666322i	−0.363195	−	0.931713i	$-0.618314\pi$
$751$	−11.5290	+	1.82601i	−0.420699	+	0.0666322i	−0.0575040	+	0.998345i	$0.518314\pi$
$752$	22.3990	+	22.3990i	0.816807	+	0.816807i
$753$		0			0
$754$	17.5598	−	12.7579i	0.639490	−	0.464617i
$755$	−3.37062	+	1.71741i	−0.122669	+	0.0625031i
$756$		0			0
$757$	37.9100	+	6.00436i	1.37786	+	0.218232i	0.801027	−	0.598628i	$-0.204287\pi$
$757$	37.9100	+	6.00436i	1.37786	+	0.218232i	0.576836	+	0.816860i	$0.304287\pi$
$758$	37.4581	+	51.5566i	1.36054	+	1.87262i
$759$		0			0
$760$	−0.625876	−	0.0991290i	−0.0227029	−	0.00359579i
$761$	−39.0623	−	28.3804i	−1.41601	−	1.02879i	−0.992415	−	0.122935i	$-0.960769\pi$
$761$	−39.0623	−	28.3804i	−1.41601	−	1.02879i	−0.423591	−	0.905854i	$-0.639231\pi$
$762$		0			0
$763$	3.07495	−	2.23408i	0.111321	−	0.0808792i
$764$	−9.53299	+	18.7095i	−0.344891	+	0.676887i
$765$		0			0
$766$	11.7197	−	1.85622i	0.423451	−	0.0670680i
$767$	−11.1224	−	5.66713i	−0.401606	−	0.204628i
$768$		0			0
$769$	1.21277	−	3.73252i	0.0437336	−	0.134598i	−0.926806	−	0.375541i	$-0.877457\pi$
$769$	1.21277	−	3.73252i	0.0437336	−	0.134598i	0.970539	+	0.240943i	$0.0774568\pi$
$770$		−	5.19130i		−	0.187082i
$771$		0			0
$772$	2.14018	−	13.5126i	0.0770269	−	0.486329i
$773$	5.21943	+	32.9542i	0.187730	+	1.18528i	0.883995	+	0.467496i	$0.154844\pi$
$773$	5.21943	+	32.9542i	0.187730	+	1.18528i	−0.696265	+	0.717784i	$0.745156\pi$
$774$		0			0
$775$	−0.873528	−	2.68844i	−0.0313781	−	0.0965717i
$776$	1.55532	−	1.55532i	0.0558329	−	0.0558329i
$777$		0			0
$778$	−4.05808			−0.145489
$779$	0.711206	+	0.414396i	0.0254816	+	0.0148473i
$780$		0			0
$781$	−1.74757	+	2.40533i	−0.0625330	+	0.0860693i
$782$	2.41535	−	2.41535i	0.0863727	−	0.0863727i
$783$		0			0
$784$	20.9004	−	6.79095i	0.746443	−	0.242534i
$785$	−7.44338	−	46.9957i	−0.265666	−	1.67735i
$786$		0			0
$787$	−10.7260	−	3.48510i	−0.382342	−	0.124230i	0.111539	−	0.993760i	$-0.464422\pi$
$787$	−10.7260	−	3.48510i	−0.382342	−	0.124230i	−0.493881	+	0.869530i	$0.664422\pi$
$788$			0.873536i			0.0311184i
$789$		0			0
$790$	24.2803	+	47.6528i	0.863855	+	1.69541i
$791$	11.0331	+	5.62164i	0.392291	+	0.199882i
$792$		0			0
$793$	2.84143	+	2.84143i	0.100902	+	0.100902i
$794$	12.5692	−	24.6684i	0.446063	−	0.875447i
$795$		0			0
$796$	0.344807	−	0.175688i	0.0122214	−	0.00622710i
$797$	−23.1041	−	16.7861i	−0.818391	−	0.594596i	0.0978602	−	0.995200i	$-0.468800\pi$
$797$	−23.1041	−	16.7861i	−0.818391	−	0.594596i	−0.916251	+	0.400604i	$0.868800\pi$
$798$		0			0
$799$	−3.94257	−	5.42648i	−0.139478	−	0.191975i
$800$	−6.77951	−	9.33119i	−0.239692	−	0.329907i
$801$		0			0
$802$	−6.61875	−	4.80880i	−0.233716	−	0.169805i
$803$	−7.52981	+	3.83663i	−0.265721	+	0.135392i
$804$		0			0
$805$	3.73680	−	7.33389i	0.131705	−	0.258486i
$806$	2.23352	+	2.23352i	0.0786723	+	0.0786723i
$807$		0			0
$808$	8.59419	+	4.37896i	0.302343	+	0.154051i
$809$	−4.83865	−	9.49639i	−0.170118	−	0.333875i	0.790169	−	0.612889i	$-0.209993\pi$
$809$	−4.83865	−	9.49639i	−0.170118	−	0.333875i	−0.960287	+	0.279013i	$0.909993\pi$
$810$		0			0
$811$		−	33.8780i		−	1.18962i	−0.803867	−	0.594809i	$-0.797228\pi$
$811$		−	33.8780i		−	1.18962i	0.803867	−	0.594809i	$-0.202772\pi$
$812$	−11.9468	−	3.88175i	−0.419250	−	0.136223i
$813$		0			0
$814$	1.12386	+	7.09577i	0.0393912	+	0.248706i
$815$	45.3739	−	14.7429i	1.58938	−	0.516421i
$816$		0			0
$817$	0.961639	−	0.961639i	0.0336435	−	0.0336435i
$818$	−9.64629	+	13.2770i	−0.337275	+	0.464219i
$819$		0			0
$820$	4.15254	+	15.7478i	0.145013	+	0.549938i
$821$	−50.1853			−1.75148			−0.875739	−	0.482785i	$-0.839625\pi$
$821$	−50.1853			−1.75148			−0.875739	+	0.482785i	$0.839625\pi$
$822$		0			0
$823$	−31.8583	+	31.8583i	−1.11051	+	1.11051i	−0.117431	+	0.993081i	$0.537466\pi$
$823$	−31.8583	+	31.8583i	−1.11051	+	1.11051i	−0.993081	+	0.117431i	$0.962534\pi$
$824$	7.80136	+	24.0101i	0.271773	+	0.836432i
$825$		0			0
$826$	3.53796	+	22.3378i	0.123101	+	0.777231i
$827$	0.559901	−	3.53508i	0.0194697	−	0.122927i	−0.976039	−	0.217595i	$-0.930179\pi$
$827$	0.559901	−	3.53508i	0.0194697	−	0.122927i	0.995509	+	0.0946679i	$0.0301789\pi$
$828$		0			0
$829$		−	18.5904i		−	0.645672i	−0.946455	−	0.322836i	$-0.895364\pi$
$829$		−	18.5904i		−	0.645672i	0.946455	−	0.322836i	$-0.104636\pi$
$830$	−9.31652	+	28.6733i	−0.323381	+	0.995265i
$831$		0			0
$832$	−2.10423	−	1.07216i	−0.0729509	−	0.0371703i
$833$	−4.59605	+	0.727944i	−0.159244	+	0.0252217i
$834$		0			0
$835$	3.41478	−	6.70188i	0.118173	−	0.231928i
$836$	0.0676503	−	0.0491508i	0.00233973	−	0.00169992i
$837$		0			0
$838$	11.1816	+	8.12394i	0.386263	+	0.280637i
$839$	35.8357	+	5.67582i	1.23719	+	0.195951i	0.740546	−	0.672006i	$-0.234567\pi$
$839$	35.8357	+	5.67582i	1.23719	+	0.195951i	0.496640	+	0.867957i	$0.334567\pi$
$840$		0			0
$841$	23.4124	+	32.2244i	0.807324	+	1.11119i
$842$	−29.8975	−	4.73529i	−1.03033	−	0.163189i
$843$		0			0
$844$	−18.7551	+	9.55622i	−0.645578	+	0.328939i
$845$	−23.3909	+	16.9945i	−0.804673	+	0.584629i
$846$		0			0
$847$	11.9979	+	11.9979i	0.412253	+	0.412253i
$848$	61.6362	−	9.76221i	2.11659	−	0.335236i
$849$		0			0
$850$	1.92773	+	3.78338i	0.0661205	+	0.129769i
$851$	−3.51997	+	10.8333i	−0.120663	+	0.371362i
$852$		0			0
$853$	−15.2753	−	4.96325i	−0.523017	−	0.169939i	0.0355971	−	0.999366i	$-0.488667\pi$
$853$	−15.2753	−	4.96325i	−0.523017	−	0.169939i	−0.558614	+	0.829428i	$0.688667\pi$
$854$	1.13891	−	7.19077i	0.0389726	−	0.246063i
$855$		0			0
$856$	16.4953	−	5.35966i	0.563799	−	0.183190i
$857$	4.88329	+	15.0292i	0.166810	+	0.513389i	0.999165	−	0.0408542i	$-0.0130079\pi$
$857$	4.88329	+	15.0292i	0.166810	+	0.513389i	−0.832355	+	0.554243i	$0.813008\pi$
$858$		0			0
$859$	−11.8857	+	16.3593i	−0.405535	+	0.558171i	−0.962122	−	0.272618i	$-0.912110\pi$
$859$	−11.8857	+	16.3593i	−0.405535	+	0.558171i	0.556587	+	0.830789i	$0.312110\pi$
$860$	26.9078			0.917548
$861$		0			0
$862$	17.4058			0.592843
$863$	6.30383	−	8.67648i	0.214585	−	0.295351i	−0.688132	−	0.725585i	$-0.741569\pi$
$863$	6.30383	−	8.67648i	0.214585	−	0.295351i	0.902717	+	0.430234i	$0.141569\pi$
$864$		0			0
$865$	−9.80418	−	30.1742i	−0.333352	−	1.02595i
$866$	54.1629	−	17.5986i	1.84053	−	0.598025i
$867$		0			0
$868$	0.285970	−	1.80554i	0.00970644	−	0.0612841i
$869$	7.58832	+	2.46560i	0.257416	+	0.0836396i
$870$		0			0
$871$	4.00387	−	12.3226i	0.135666	−	0.417537i
$872$	−1.94635	−	3.81993i	−0.0659118	−	0.129359i
$873$		0			0
$874$	0.409948	−	0.0649294i	0.0138667	−	0.00219627i
$875$	−8.21584	−	8.21584i	−0.277746	−	0.277746i
$876$		0			0
$877$	9.77788	−	7.10405i	0.330176	−	0.239887i	−0.410330	−	0.911937i	$-0.634586\pi$
$877$	9.77788	−	7.10405i	0.330176	−	0.239887i	0.740505	+	0.672051i	$0.234586\pi$
$878$	−56.2880	+	28.6802i	−1.89963	+	0.967908i
$879$		0			0
$880$	−9.26506	−	1.46744i	−0.312325	−	0.0494674i
$881$	−5.54253	−	7.62863i	−0.186732	−	0.257015i	0.705379	−	0.708830i	$-0.250777\pi$
$881$	−5.54253	−	7.62863i	−0.186732	−	0.257015i	−0.892112	+	0.451815i	$0.850777\pi$
$882$		0			0
$883$	−23.2136	−	3.67668i	−0.781200	−	0.123730i	−0.246918	−	0.969036i	$-0.579418\pi$
$883$	−23.2136	−	3.67668i	−0.781200	−	0.123730i	−0.534282	+	0.845306i	$0.679418\pi$
$884$	−1.22616	−	0.890856i	−0.0412402	−	0.0299627i
$885$		0			0
$886$	−42.7752	+	31.0780i	−1.43706	+	1.04409i
$887$	22.0210	−	43.2187i	0.739394	−	1.45114i	−0.147448	−	0.989070i	$-0.547106\pi$
$887$	22.0210	−	43.2187i	0.739394	−	1.45114i	0.886842	−	0.462073i	$-0.152894\pi$
$888$		0			0
$889$	9.92789	−	1.57242i	0.332971	−	0.0527374i
$890$	11.9348	+	6.08107i	0.400055	+	0.203838i
$891$		0			0
$892$	1.18242	−	3.63912i	0.0395904	−	0.121847i
$893$		−	0.815032i		−	0.0272740i
$894$		0			0
$895$	−1.80293	+	11.3833i	−0.0602654	+	0.380500i
$896$	3.15531	+	19.9218i	0.105411	+	0.665542i
$897$		0			0
$898$	15.6988	+	48.3161i	0.523877	+	1.61233i
$899$	−7.08296	+	7.08296i	−0.236230	+	0.236230i
$900$		0			0
$901$	−13.2140			−0.440221
$902$	6.57201	+	3.82929i	0.218824	+	0.127501i
$903$		0			0
$904$	8.20974	−	11.2997i	0.273052	−	0.375824i
$905$	8.88248	−	8.88248i	0.295264	−	0.295264i
$906$		0			0
$907$	−8.16520	+	2.65304i	−0.271121	+	0.0880926i	−0.441422	−	0.897299i	$-0.645526\pi$
$907$	−8.16520	+	2.65304i	−0.271121	+	0.0880926i	0.170301	+	0.985392i	$0.445526\pi$
$908$	−3.17090	−	20.0202i	−0.105230	−	0.664395i
$909$		0			0
$910$	−10.8736	−	3.53305i	−0.360456	−	0.117119i
$911$		−	21.0427i		−	0.697176i	−0.937276	−	0.348588i	$-0.886661\pi$
$911$		−	21.0427i		−	0.697176i	0.937276	−	0.348588i	$-0.113339\pi$
$912$		0			0
$913$	2.04197	+	4.00760i	0.0675794	+	0.132632i
$914$	−11.5989	−	5.90994i	−0.383658	−	0.195483i
$915$		0			0
$916$	−6.57638	−	6.57638i	−0.217290	−	0.217290i
$917$	0.531129	−	1.04240i	0.0175394	−	0.0344231i
$918$		0			0
$919$	42.6461	−	21.7293i	1.40676	−	0.716782i	0.424700	−	0.905334i	$-0.360379\pi$
$919$	42.6461	−	21.7293i	1.40676	−	0.716782i	0.982063	+	0.188552i	$0.0603794\pi$
$920$	−7.51114	−	5.45716i	−0.247635	−	0.179917i
$921$		0			0
$922$	−25.4769	−	35.0659i	−0.839037	−	1.15484i
$923$	3.84880	+	5.29742i	0.126685	+	0.174367i
$924$		0			0
$925$	−11.4556	−	8.32298i	−0.376658	−	0.273658i
$926$	22.5215	−	11.4753i	0.740103	−	0.377101i
$927$		0			0
$928$	−18.5550	+	36.4163i	−0.609099	+	1.19542i
$929$	36.8866	+	36.8866i	1.21021	+	1.21021i	0.970957	+	0.239254i	$0.0769028\pi$
$929$	36.8866	+	36.8866i	1.21021	+	1.21021i	0.239254	+	0.970957i	$0.423097\pi$
$930$		0			0
$931$	−0.503802	−	0.256700i	−0.0165115	−	0.00841300i
$932$	−0.548327	−	1.07615i	−0.0179610	−	0.0352505i
$933$		0			0
$934$			37.9253i			1.24096i
$935$	1.88909	+	0.613801i	0.0617797	+	0.0200735i
$936$		0			0
$937$	2.38729	+	15.0727i	0.0779893	+	0.492405i	0.995505	+	0.0947061i	$0.0301911\pi$
$937$	2.38729	+	15.0727i	0.0779893	+	0.492405i	−0.917516	+	0.397699i	$0.869809\pi$
$938$	−22.3258	+	7.25409i	−0.728963	+	0.236855i
$939$		0			0
$940$	11.4028	−	11.4028i	0.371918	−	0.371918i
$941$	−32.5243	+	44.7658i	−1.06026	+	1.45932i	−0.180701	+	0.983538i	$0.557837\pi$
$941$	−32.5243	+	44.7658i	−1.06026	+	1.45932i	−0.879561	+	0.475787i	$0.842163\pi$
$942$		0			0
$943$	6.52804	+	10.1404i	0.212582	+	0.330217i
$944$	40.8669			1.33011
$945$		0			0
$946$	8.88617	−	8.88617i	0.288914	−	0.288914i
$947$	0.485672	+	1.49474i	0.0157822	+	0.0485727i	0.958637	−	0.284630i	$-0.0918707\pi$
$947$	0.485672	+	1.49474i	0.0157822	+	0.0485727i	−0.942855	+	0.333203i	$0.891871\pi$
$948$		0			0
$949$	2.91156	+	18.3829i	0.0945133	+	0.596734i
$950$	−0.0807133	+	0.509604i	−0.00261869	+	0.0165337i
$951$		0			0
$952$		−	3.10441i		−	0.100615i
$953$	−13.1845	+	40.5778i	−0.427089	+	1.31444i	0.473891	+	0.880584i	$0.342849\pi$
$953$	−13.1845	+	40.5778i	−0.427089	+	1.31444i	−0.900980	+	0.433861i	$0.857151\pi$
$954$		0			0
$955$	−54.0021	−	27.5154i	−1.74747	−	0.890379i
$956$	−6.57981	+	1.04214i	−0.212806	+	0.0337052i
$957$		0			0
$958$	12.3626	−	24.2629i	0.399416	−	0.783898i
$959$	24.3495	−	17.6909i	0.786285	−	0.571270i
$960$		0			0
$961$	23.9002	+	17.3645i	0.770975	+	0.560146i
$962$	15.6275	+	2.47515i	0.503851	+	0.0798022i
$963$		0			0
$964$	−5.95234	−	8.19270i	−0.191712	−	0.263869i
$965$	39.0019	+	6.17730i	1.25552	+	0.198854i
$966$		0			0
$967$	3.68798	−	1.87912i	0.118597	−	0.0604284i	−0.393685	−	0.919245i	$-0.628800\pi$
$967$	3.68798	−	1.87912i	0.118597	−	0.0604284i	0.512283	+	0.858817i	$0.328800\pi$
$968$	15.4836	−	11.2495i	0.497663	−	0.361573i
$969$		0			0
$970$	−3.97082	−	3.97082i	−0.127495	−	0.127495i
$971$	−15.8383	+	2.50854i	−0.508276	+	0.0805030i	−0.405305	−	0.914181i	$-0.632835\pi$
$971$	−15.8383	+	2.50854i	−0.508276	+	0.0805030i	−0.102971	+	0.994684i	$0.532835\pi$
$972$		0			0
$973$	−4.64475	−	9.11584i	−0.148904	−	0.292240i
$974$	11.1447	−	34.2997i	0.357098	−	1.09903i
$975$		0			0
$976$	−12.5116	−	4.06528i	−0.400488	−	0.130126i
$977$	−6.69308	+	42.2584i	−0.214131	+	1.35197i	0.613056	+	0.790039i	$0.289940\pi$
$977$	−6.69308	+	42.2584i	−0.214131	+	1.35197i	−0.827187	+	0.561927i	$0.810060\pi$
$978$		0			0
$979$	1.90052	−	0.617515i	0.0607408	−	0.0197359i
$980$	−3.45711	−	10.6399i	−0.110433	−	0.339878i
$981$		0			0
$982$	0.0545251	−	0.0750473i	0.00173997	−	0.00239486i
$983$	31.6046			1.00803			0.504015	−	0.863695i	$-0.331856\pi$
$983$	31.6046			1.00803			0.504015	+	0.863695i	$0.331856\pi$
$984$		0			0
$985$	−2.52132			−0.0803360
$986$	8.84409	−	12.1728i	0.281653	−	0.387662i
$987$		0			0
$988$	−0.0569095	−	0.175150i	−0.00181053	−	0.00557225i
$989$	18.9502	−	6.15728i	0.602580	−	0.195790i
$990$		0			0
$991$	4.28861	−	27.0772i	0.136232	−	0.860137i	−0.821024	−	0.570894i	$-0.806597\pi$
$991$	4.28861	−	27.0772i	0.136232	−	0.860137i	0.957256	−	0.289242i	$-0.0934034\pi$
$992$	−5.65670	−	1.83797i	−0.179601	−	0.0583558i
$993$		0			0
$994$	3.66600	−	11.2828i	0.116278	−	0.357868i
$995$	0.507096	+	0.995231i	0.0160760	+	0.0315510i
$996$		0			0
$997$	24.5211	−	3.88375i	0.776590	−	0.123000i	0.244456	−	0.969660i	$-0.421391\pi$
$997$	24.5211	−	3.88375i	0.776590	−	0.123000i	0.532133	+	0.846661i	$0.321391\pi$
$998$	−39.4001	−	39.4001i	−1.24719	−	1.24719i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	369.2.u.a.361.3		24
3.2	odd	2		41.2.g.a.33.1	yes	24
12.11	even	2		656.2.bs.d.33.1		24
41.5	even	20	inner	369.2.u.a.46.3		24
123.5	odd	20		41.2.g.a.5.1	✓	24
123.95	even	40		1681.2.a.m.1.3		24
123.110	even	40		1681.2.a.m.1.4		24
492.251	even	20		656.2.bs.d.497.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.5.1	✓	24	123.5	odd	20
41.2.g.a.33.1	yes	24	3.2	odd	2
369.2.u.a.46.3		24	41.5	even	20	inner
369.2.u.a.361.3		24	1.1	even	1	trivial
656.2.bs.d.33.1		24	12.11	even	2
656.2.bs.d.497.1		24	492.251	even	20
1681.2.a.m.1.3		24	123.95	even	40
1681.2.a.m.1.4		24	123.110	even	40

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 369 = 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	369.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00762 - 1.38687i) q^{2} +(-0.290083 - 0.892782i) q^{4} +(2.57687 - 0.837277i) q^{5} +(-0.252316 + 1.59306i) q^{7} +(1.73027 + 0.562198i) q^{8} +O(q^{10})\)	\(q+(1.00762 - 1.38687i) q^{2} +(-0.290083 - 0.892782i) q^{4} +(2.57687 - 0.837277i) q^{5} +(-0.252316 + 1.59306i) q^{7} +(1.73027 + 0.562198i) q^{8} +(1.43532 - 4.41746i) q^{10} +(-0.314590 - 0.617417i) q^{11} +(-1.50733 + 0.238738i) q^{13} +(1.95513 + 1.95513i) q^{14} +(4.04205 - 2.93672i) q^{16} +(-0.942631 + 0.480295i) q^{17} +(-0.126968 - 0.0201098i) q^{19} +(-1.49501 - 2.05771i) q^{20} +(-1.17327 - 0.185828i) q^{22} +(-1.52374 - 1.10707i) q^{23} +(1.89416 - 1.37619i) q^{25} +(-1.18772 + 2.33104i) q^{26} +(1.49545 - 0.236856i) q^{28} +(-7.39222 - 3.76652i) q^{29} +(0.373094 - 1.14827i) q^{31} -4.92630i q^{32} +(-0.283709 + 1.79127i) q^{34} +(0.683646 + 4.31637i) q^{35} +(-1.86889 - 5.75186i) q^{37} +(-0.155826 + 0.155826i) q^{38} +4.92939 q^{40} +(-5.96866 - 2.31844i) q^{41} +(-6.21829 + 8.55874i) q^{43} +(-0.459962 + 0.459962i) q^{44} +(-3.07072 + 0.997738i) q^{46} +(0.991818 + 6.26210i) q^{47} +(4.18322 + 1.35921i) q^{49} -4.01364i q^{50} +(0.650391 + 1.27646i) q^{52} +(11.1289 + 5.67046i) q^{53} +(-1.32761 - 1.32761i) q^{55} +(-1.33219 + 2.61457i) q^{56} +(-12.6723 + 6.45684i) q^{58} +(6.61738 + 4.80781i) q^{59} +(-1.54768 - 2.13021i) q^{61} +(-1.21656 - 1.67445i) q^{62} +(1.25193 + 0.909582i) q^{64} +(-3.68431 + 1.87725i) q^{65} +(-3.85439 + 7.56467i) q^{67} +(0.702239 + 0.702239i) q^{68} +(6.67512 + 3.40115i) q^{70} +(-1.94789 - 3.82296i) q^{71} -12.1957i q^{73} +(-9.86025 - 3.20379i) q^{74} +(0.0188776 + 0.119188i) q^{76} +(1.06296 - 0.345376i) q^{77} +(-8.14191 + 8.14191i) q^{79} +(7.95700 - 10.9519i) q^{80} +(-9.22954 + 5.94167i) q^{82} -6.49090 q^{83} +(-2.02690 + 2.02690i) q^{85} +(5.60421 + 17.2480i) q^{86} +(-0.197214 - 1.24516i) q^{88} +(-0.451128 + 2.84831i) q^{89} -2.46150i q^{91} +(-0.546357 + 1.68151i) q^{92} +(9.68412 + 4.93431i) q^{94} +(-0.344018 + 0.0544871i) q^{95} +(0.548878 - 1.07723i) q^{97} +(6.10017 - 4.43203i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

Introduction

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